Cyclic testing of Q690 circular high-strength concrete-filled thin-walled steel tubular columns

Abstract

Under seismic action, the severe damage in critical regions of structures could be ascribed to the cumulative damage caused by cyclic loading. This article describes an investigation of the hysteresis behaviour of Q690 circular high-strength concrete-filled thin-walled steel tubular columns with out-of-code diameter-to-thickness ratios. A total of eight specimens were tested under constant axial compression and cyclic lateral loading. The study results of phase I testing consisting of a benchmark test were summarized to examine the seismic behaviour under standard loading, and those of the phase II testing that considered different fatigue loading modes and different concrete strengths were summarized to investigate the low-cycle fatigue behaviour. The load–displacement hysteretic curves, energy dissipation, strength and stiffness degradation were discussed in detail. A simplified method was proposed to predict the low-cycle fatigue life, which can be applied in the damage-based seismic design of circular concrete-filled steel tubular structures.

Keywords

cyclic loading energy dissipation failure modes low-cycle fatigue Q690 circular high-strength concrete-filled thin-walled steel tubular columns

Introduction

Concrete-filled steel tubular (CFST) columns, as a relatively new type of structural member, are inescapably threatened with potential earthquake risks despite possessing remarkable mechanical properties, namely, high strength (HS), high ductility and greater energy dissipation capacity (Elremaily and Azizinamini, 2002; Varma et al., 2002a; Wang et al., 2017). During an earthquake, the severe failure in the plastic hinge regions of CFST columns is due to the cumulative damage of the steel tube caused by the repeated cyclic loading in the post-yield strain range (Boyd et al., 1995; Elchalakani et al., 2004). To examine the seismic behaviour of CFST columns, earlier significant quasi-static cyclic loading experiments have been conducted by many researchers, such as Usami and Ge (1994), Ge and Usami (1996), Hajjar and Gourley (1997), Nakanishi et al. (1999), Marson and Bruneau (2000), Fam et al. (2004), Han et al. (2005) and Han and Yang (2006). These researchers made great efforts to help understand the seismic behaviour of CFST columns through varying different parameters.

Recently, with the advent of HS steel and the progress in the welding technique, the application of HS steel (yield strength of $f_{y} \geq 600 MPa$ ) has attracted much attention worldwide (Li et al., 2015; Varma et al., 2002b). Compared with conventional steel, HS steel could provide a larger elastic deformation capacity and better confined effect for CFST columns, and the local buckling could be delayed until a large rotation (Skalomenos et al., 2016). Because of the application of HS materials, the section size of traditional CFST columns could be diminished to obtain a favourable architectural aesthetic effect and gain further economic benefits under the premise of ensuring the mechanical property; thus, the high-strength concrete-filled thin-walled steel tubular (HCFTST) columns begin to develop gradually.

However, the aforementioned studies mainly focused on the hysteresis behaviour of traditional CFST columns under standard cyclic loading with increasing peak drift deformation (Gajalakshmi and Helena, 2012; Zhang et al., 2009b). Regarding the HCFTST columns, studies on the effects of the amplitudes, number of cycles and loading modes on the damage accumulation are lacking. In fact, many structures would collapse after peak earthquake acceleration with few inelastic cycles, suggesting that the low-cycle fatigue damage is not negligible and the effects of amplitude and cyclic numbers should be noticeable (EI-Bahy et al., 1999; Zhang et al., 2009a). Therefore, more experimental research studies are required in this area, mainly focusing on the HS and thin-walled steel tubes, to further clarify the influences of cyclic behaviour on HCFTST columns. Furthermore, more test data are also required for the design codes, which currently restrict the use of HS materials in CFST columns because of the limited knowledge.

So far, no consensus has been reached on the definition of HCFTST columns. Against this background, a new out-of-code column, namely, the Q690 circular HCFTST column, was proposed in this article; this column comprised ultrahigh-strength Q690 steel (yield strength of $f_{y} > 690 MPa$ ) and HS concrete (cylinder compressive strength of $f_{c} \geq 60 MPa$ ), and had large diameter-to-thickness (D/t) ratios outside of the limitations in the current design codes, for example, American AISC-360-10 $(D / t \leq (0.15 E_{s} / f_{y}))$ and Chinese GB 50936-2014 $(D / t \leq (31, 725 / f_{y}))$ . In this study, a total of eight Q690 circular HCFTST columns were tested to investigate the cyclic behaviour. This presents the results of phase I tests consisting of benchmark test to examine the seismic behaviour under standard loading and the phase II tests to investigate the low-cycle fatigue behaviour. The tested parameters are axial compression ratio (n), loading modes and concrete strength. The strength, ductility, stiffness degradation and dissipated energy of the specimens were experimentally investigated and analysed. A simplified method was proposed to predict the low-cycle fatigue life based on the Manson–Coffin model (Coffin, 1953; Manson, 1953; Manson and Halford, 1981). The main objectives of the research are as follows: (1) to provide a new series of test data for the HCFTST columns, (2) to evaluate the cyclic behaviour of the specimens under tested parameters and (3) to predict the low-cycle fatigue lives of CFST columns.

Experimental programme

Material properties

The ultrahigh-strength Q690 steel from the same batch was adopted in this study. According to the ‘Metallic materials-Tensile testing at ambient temperature’ (GB/T 228-2002), the coupon test was conducted to obtain the properties of Q690 steel, as shown in Figure 1. The yield strength $(f_{y})$ and ultimate strength $(f_{u})$ were 723 and 765 MPa, respectively, and the elastic modulus $(E_{s})$ and Poisson’s ratio $(v_{s})$ were 222,010 MPa and 0.281, respectively.

Figure 1.

Tensile coupon test.

Both normal-strength (NS) and HS concrete were utilized in this article. The reserved concrete blocks for the compressive strength test were maintained under the same condition with tested columns. Table 1 lists the actual cylinder strengths $(f_{c})$ and the mix proportions of the concrete.

Table 1.

Details of concrete.

Concrete grade	$f_{c} (MPa)$	Cement (kg/m³)	Fine aggregate (kg/m³)	Coarse aggregate (kg/m³)	Water (kg/m³)	Silica fume (kg/m³)	Water reducer (kg/m³)
NS-1	43.5	360 (Portland 425)	733	1084	170	–	13.2
NS-2	49.1	420 (Portland 425)	700	1250	135	–	12
HS-1	78.6	301 (Portland 425)	640	1310	129	129	13
HS-2	97.6	315 (Portland 525)	585	1365	120	135	13

‘NS’ and ‘HS’ denote normal-strength and high-strength, and ‘Portland 425’ and ‘Portland 525’ indicate the cement grade, respectively.

Specimen design and preparation

According to Chinese GB 50936-2014 $(D / t \leq (31725 / f_{y}))$ , the maximum D/t ratio of Q690 HCFTST columns is 44. Considering the limitations of the test setups and the manufacture difficulty in HS thin-walled steel tubes, the maximum out-of-code D/t ratios of Q690 circular HCFTST columns were determined as 70 and 130, respectively. The tests were conducted in two phases. Phase I testing consisted of benchmark tests under standard cyclic loading, and phase II testing involved low-cycle fatigue loading tests. A summary of tested specimens is presented in Table 2.

Table 2.

Summary of tested specimens.

Test phase	Specimen	D (mm)	t (mm)	$f_{y} (MPa)$	D/t ratio	$f_{c} (MPa)$	n	Loading patterns
I	CFST-1-1	140	2	723	70	78.6	0.18	Variable pattern 1
	CFST-1-2	140	2	723	70	78.6	0.27	Variable pattern 1
	CFST-1-3	260	2	723	130	97.6	0.36	Variable pattern 1
	CFST-1-4	260	2	723	130	97.6	0.09	Variable pattern 1
II	CFST-2-1	140	2	723	70	78.6	0.27	Constant pattern 1
	CFST-2-2	140	2	723	70	78.6	0.27	Constant pattern 2
	CFST-2-3	140	2	723	70	78.6	0.27	Variable pattern 2
	CFST-2-4	140	2	723	70	49.1	0.27	Variable pattern 2

CFST: concrete-filled steel tubular.

In Table 2, the axial compression ratio (n) was defined as

n = P / P_{0}

(1)

where P is the axial load applied on the HCFTST columns and P₀ is the nominal squash load calculated by the following equation

P_{0} = A_{s} f_{y} + 0.85 A_{c} f_{c}

(2)

where $A_{s}$ and $A_{c}$ are the cross-sectional areas of the steel tube and core concrete, respectively.

Figure 2 shows the design details of the Q690 circular HCFTST columns. The clear height of the HCFTST column was 525 mm, and a reinforced concrete (RC) foundation was cast together with the column, representing a relative rigid member, such as a beam–column connection. High-strength steel bars (HSBs, $f_{y} = 1000 MPa$ ) and stiffening ribs were used to strengthen the RC foundations.

Figure 2.

Details of the tested specimens.

The construction process of specimens is shown in Figure 3. The steel tubes and the reinforcements of the foundations were fabricated first. Afterwards, the concrete inside steel tubes was cast, and the autoclaved curing technology at high temperature was employed to ensure the qualities of the HS concrete. Subsequently, the stiffening ribs and the reinforcements were assembled. Next, the concrete of RC foundation was poured, and then, the end plates II were finally welded.

Figure 3.

Specimen preparation.

Test setup and instrumentation

All the specimens were tested in the experimental setup shown in Figure 4. The RC foundation was attached to the ground tightly with pressure beams and anchor stocks, while two adjustable seats were installed to prevent the lateral sliding of the specimen. The axial compression was imposed on the column through a hydraulic jack of 2000-kN capacity. Furthermore, the triangular box connector was assembled using HS bolts (Grade 12.9, M28) for cyclic loading using a 1000-kN MTS actuator. A total of 12 bidirectional strain gauges, divided into three layers, were mounted on the steel tubes to monitor the longitudinal and circumferential deformation in an equal-interval layout along the circumferential direction. The space between every two layers was half of the diameter of the tested columns, and the lowest layer was 30 mm away from the top surface of the RC foundation. The horizontal load and displacement were automatically recorded by the MTS actuator. The axial force was monitored by the pressure transducers fixed on the jack.

Figure 4.

Test setup: (a) schematic diagram of the test devices and (b) test photograph.

Test procedures

The quasi-static cyclic loading method was adopted in this study. First, the preloading procedure was conducted to ensure the equipment functioned normally. If all was in order, then the axial load was applied first to the targeted value and then was kept constant during testing. Afterwards, the lateral force of different loading patterns was cycled under the displacement control mode, as shown in Figure 5.

Figure 5.

Loading patterns: (a) variable pattern 1, (b) variable pattern 2, (c) constant pattern 1 and (d) constant pattern 2.

During the phase I testing, for ‘variable pattern 1’, four single cycles with peak drift ratios of $Δ / L$ 0.10%, 0.25%, 0.50% and 0.75% were initially applied, where ‘Δ’ indicates the lateral displacement and ‘L’ denotes the column length. Next, three cycles were exerted at each drift ratio level from 1% to 8%. Moreover, if there was no evident failure after drift ratio 8%, then the test would be continued by applying drift ratio 10% until the failure of specimen.

During the phase II testing, for ‘variable pattern 2’, the drift ratio increased from 1% to 6%, with application of one cycle at each deflection, and then, the drift ratio decreased to 1% after reaching peak lateral deformation. Moreover, the constant amplitude loading patterns at drift ratio 4% and 6% were utilized to examine low-cycle fatigue behaviour of the Q690 circular HCFTST columns. The test ended when the specimen was unable to sustain the targeted axial force or lateral cyclic loading because of the severe steel fracture and concrete crushing.

Experimental observations and failure modes

During the phase I testing, through the statistics of the test phenomena, very slight local buckling emerged at drift ratios of 2%–3% in the compressive sides of the column bases, except for the specimen CFST-1-4, for which this buckling occurred during the first cycle of drift ratio 4%. On the reverse excursion, slight buckling was also observed on the other side. From then onwards, the buckling on both sides of the columns continued to develop with the steel ductility until the 7%–8% drift, when small hairline cracks on the tensile side of the steel tube could be observed but did not penetrated the steel tube; with continued loading, the cracks developed to penetrate the steel shell, accompanied by a loud sound. Finally, the test ended owing to the severe rupture of steel tube and crushing of the core concrete.

In phase II testing, the specimen CFST-2-1 had slight local buckling growing gradually at the column base, and the first crack of steel tube appeared at the 31th cycle; at the 50th cycle, the test ended owing to severe failure. The slight local buckling of CFST-2-2 emerged at the first cycle and magnified more rapidly than CFST-2-1; the steel tube fractured first at the 11th cycle until the severe failure appeared at 20th cycle. The specimen CFST-2-3 subjected to ‘variable pattern 2’ had slight local buckling at the third cycle, and the first hairline crack occurred at 14th cycle. With loading continuously, the apparent cracking of steel tube could be noticed at 19th cycle until the test ended at the 44th cycle. For CFST-2-4, the slight local buckling emerged at the second cycle, and the first crack in tensile side of steel tube could be seen at 17th cycle; the test ended at the 44th cycle.

A summary of the failure modes for all HCFTST columns, including the concrete crushing, severe fracture and local buckling of steel tube at column bases, is described in Figure 6. In Figure 6(a), an elephant-foot-shaped buckling in the column base is shown. As shown in Figure 6(b) and (c), the rupture crack apparently penetrated through the tube thickness, and the pulverized concrete spilled out through the rupture in the buckled region as the rupture crack width increased. For all specimens, the buckling was observed at nearly the same heights (H = 20 mm) above the foundation surface, as shown in Figure 6(d).

Figure 6.

Failure modes: (a) local buckling, (b) concrete crushing, (c) steel fracture and (d) cracking height.

It should be noted that although the failure modes of the phase I and phase II testing are similar, the induced factors of local buckling, concrete crushing and steel fracture are completely different. In phase I testing, the adverse $P - Δ$ effect on the bottom of the cantilever column increased gradually with the increase in the drift ratios, and the transcending failure together with the cumulative damage coexisted. After reaching the peak load, the transcending failure almost dominated so that the compressive zone of concrete decreased sharply. Finally, the core concrete was crushed, and transverse cracks in the cross section were gradually formed. The excessive lateral displacement also promoted the rupture of the steel tube because of the strength failure. In phase II testing, the cumulative damage was dominant mostly because the imposed drift ratios do not exceed the ultimate displacement. Under the reciprocating low-cycle load, the core concrete and thin-walled steel tube experienced low-cycle fatigue damage, which eventually lead to the fatigue failure, namely, concrete crushing and steel rupture.

Analysis of the experimental results

Load–displacement hysteretic curve

Phase I testing

Figure 7 depicts the hysteretic curves of phase I testing. An initial elastic response was observed for all specimens, and then, the columns entered the elastic–plastic process accompanied by the gradual strength and stiffness degradation. For specimens with D/t = 70 (CFST-1-1 and CFST-1-2), with the increase in drift level, apparent softening platforms existed in hysteretic curves when the lateral load turned from unloading to reloading. The slight pinching observed in the hysteresis curve may be due to the opening and subsequent closing of horizontal concrete cracks transverse to the columns axis. As shown in Figure 7(c) and (d), the hysteretic loops of CFST-1-4 were narrower and thus have a lower energy dissipation capacity than those of the CFST-1-3 due to the loss of the confined effect under the lower axial compression. Hence, for Q690 circular HCFTST columns with D/t ratio exceeding current codes, increasing the axial compression ratio is an efficient method to improve the potential of HS materials by providing an excellent confined action to limit the propagation of the concrete shear cracks. Overall, the Q690 circular HCFTST columns with reasonable design could display favourable hysteresis behaviour and could be expected to have a widespread application in earthquake-prone regions.

Figure 7.

Hysteretic curves in phase I testing: (a) CFST-1-1, (b) CFST-1-2, (c) CFST-1-3 and (d) CFST-1-4.

Phase II testing

Figure 8 shows the hysteresis curves of phase II testing. Under constant amplitude loading, the hysteretic loops of CFST-2-1 and CFST-2-2 shrank gradually, accompanied by the stiffness degradation and strength reduction. The plots indicated that the larger deformation amplitude could result in severe damage. With regard to CFST-2-3 and CFST-2-4 under ‘variable pattern 2’, the asymmetric phenomenon occurred after accomplishing a total cycle via the existing residual deformation of the transcendental damage. The concrete strength had little effect on the cyclic numbers, and from the plots aforementioned, the loading history governed the development tendency of the cumulative damage.

Figure 8.

Hysteretic curves in phase II testing: (a) CFST-2-1, (b) CFST-2-2, (c) CFST-2-3 and (d) CFST-2-4.

Strength analysis

The skeleton curves of phase I testing shown in Figure 9 were constructed by connecting the maximum load point at each displacement level according to the load–displacement hysteretic curves. To evaluate the seismic resistance, the general yield moment (GYM) method (Zhou et al., 2012) was adopted to obtain the yield point $(Δ y, P_{y})$ . In addition, the point $(Δ m, P_{m})$ is the peak point determined by maximum lateral load, and the ultimate failure point is defined as $(Δ u, P_{u})$ , where $Δ u$ is the displacement when the load decreases to $P_{u} = 0.85 P_{m}$ . All characteristic values in phase I testing obtained by averaging the values of the push and pull directions are shown in Table 3. Compared with CFST-1-1, the yield load of CFST-1-2 decreased by 7.5% and the peak load increased by 2.9%; moreover, the yield and peak load of CFST-1-4 reduced by 0.1% and 0.6%, respectively, compared to CFST-1-3.

Figure 9.

Skeleton curves.

Table 3.

Characteristic values of phase I testing.

Specimen	$Δ y (mm)$	$P_{y} (kN)$	$Δ m (mm)$	$P_{m} (kN)$	$Δ u (mm)$	$P_{u} (kN)$
CFST-1-1	13.79	99.72	28.32	115.27	39.77	98.12
CFST-1-2	14.47	92.22	28.88	118.61	47.64	101.02
CFST-1-3	15.07	261.86	26.25	297.06	43.11	252.50
CFST-1-4	18.04	260.00	28.88	295.67	36.75	251.32

CFST: concrete-filled steel tubular.

Moreover, the strength degradation factor $(S_{dj})$ at overall loads was also introduced to explore the global strength degradation characteristics of tested specimens during the whole loading process and is expressed as follows

S_{dj} = P_{j} / P_{m}

(3)

where $P_{j}$ is the maximum horizontal load under the jth drift ratio. The relationship between the strength degradation factor $(S_{dj})$ and the relative horizontal displacement $(Δ / Δ y)$ is illustrated in Figure 10(a).

Figure 10.

Strength degradation: (a) phase I testing and (b) phase II testing.

For the Q690 circular HCFTST columns, the strength degradation factor at the overall loads raised gradually with the increase in $Δ / Δ y$ ; when the maximum carrying capacity is exceeded, $S_{dj}$ reduces gradually with the increase in $Δ / Δ y$ . The strength degradation factor at the first cycle of 8% drift ratio was used for unified comparisons. Compared with the specimen CFST-1-1, the strength degradation factor in the positive direction and the negative direction of CFST-1-2 increased by 30.6% and 4.4%, respectively. Likewise, the degradation factors of CFST-1-3 (compared to those of CFST-1-4) increased by 22.8% and 16.1%, respectively. That result is due to the stronger confined effect under a higher axial compression ratio.

The strength degradation in phase II testing is shown in Figure 10(b), in which the specimens under different loading patterns had an approximately linear descending tendency. Moreover, the strength degradation factors of specimen CFST-2-1 as fatigue failure emerges are 0.81 and 0.88 in the positive and negative directions, respectively. Regarding the CFST-2-2, the factors are 0.79 and 0.78, respectively. Note that the reduction in strength was not caused by the imposed displacement beyond the ultimate value but the cumulative damage induced by the low-cycle fatigue phenomenon.

Inter-story drift angle and ductility

The inter-story drift angle and ductility coefficient were used to evaluate the ductility of Q690 circular HCFTST columns. In Table 4, the inter-story drift angle can be expressed by $θ = Δ / L$ . $θ_{y}$ , $θ_{m}$ and $θ_{u}$ are the drift angle at yield, peak and failure, respectively. The ductility coefficient u can be calculated by $u = Δ u / Δ y$ based on the data in Table 3.

Table 4.

Details of ductility.

Specimen	$θ_{y}$	$θ_{m}$	$θ_{u}$	u
CFST-1-1	0.0263	0.0539	0.0758	2.88
CFST-1-2	0.0276	0.0550	0.0907	3.30
CFST-1-3	0.0287	0.0500	0.0821	2.86
CFST-1-4	0.0344	0.0550	0.0700	2.04

CFST: concrete-filled steel tubular.

The Chinese technical code for CFST structures GB 50936-2014 specifies the requirement on the ductility for CFST structures: the limits of allowable elastic inter-story drift angle $(θ_{y})$ and elastic–plastic inter-story drift angle $(θ_{u})$ are 1/300 (0.0033 rad) and 1/50 (0.02 rad), respectively. For the Q690 circular HCFTST columns in this article, the yield drift angle $(θ_{y})$ and ultimate drift angle $(θ_{u})$ are within the ranges of 0.0263–0.0344 and 0.0700–0.0907, respectively. The results of Tables 3 and 4 indicate that the HCFTST columns could display favourable deformation capacity though the ductility coefficient is smaller than that of the traditional CFST columns (Elremaily and Azizinamini, 2002; Fam et al., 2004; Gajalakshmi and Helena, 2012). Moreover, the HS concrete often exhibits obvious brittleness compared to NS concrete. Under out-of-code D/t ratios, the smaller axial compression ratio $(n \leq 0.36)$ tends to cause insufficient confined effect for the HS core concrete, which can exacerbate the extension of the concrete cracks under cyclic loading. As a result, the effective compression zone of the concrete gradually shrinks and the concrete in tension zone fails prematurely. The contribution of core concrete to the flexural stiffness is reduced for the columns with smaller axial compression ratios. Therefore, the bearing capacity and ductility of the specimens slightly decrease with the reduction of axial compression ratio (e.g. CFST-1-3 and CFST-1-4). Overall, the Q690 circular HCFTST columns could satisfy the requirement of the Chinese seismic design code and are applicable for buildings located in earthquake-prone regions.

Energy dissipation capacity

In this section, energy dissipation analysis was conducted to reveal the cumulative damage regularities under various loading patterns. The hysteretic energy of every loop could be obtained by the area integral. In phase I testing, for comparison purposes, the dissipated energy can be normalized as (Zhu et al., 2016)

E_{N} = \sum_{i = 1}^{n} [E_{i} / (F_{i} Δ_{i})]

(4)

Δ_{i} = (Δ_{i}^{+} - Δ_{i}^{-}) / 2, F_{i} = (F_{i}^{+} - F_{i}^{-}) / 2

(5)

where $E_{N}$ is the normalized dissipated energy; $Δ_{i}^{+}$ and $Δ_{i}^{-}$ are the maximum tip displacements of the ith loop in the positive and negative direction, respectively; and $F_{i}^{+}$ and $F_{i}^{-}$ are the lateral forces corresponding to $Δ_{i}^{+}$ and $Δ_{i}^{-}$ , respectively. The cumulative dissipated energy $(E_{T})$ and the normalized dissipated energy (until 8% drift ratio) for specimens in phase I testing are listed in Table 5; the CFST-1-4 exhibited lower energy dissipation capacity $(E_{N} = 17.51)$ than the others (E_N = 26.67–32.37) owing to the high D/t = 130 and small compression ratio (n = 0.09).

Table 5.

Energy dissipation of phase I testing.

Specimen	$E_{T} (kN mm)$	$E_{N}$
CFST-1-1	76,961.10	32.37
CFST-1-2	68,517.09	29.72
CFST-1-3	159,123.02	26.67
CFST-1-4	87,726.34	17.51

CFST: concrete-filled steel tubular.

The energy dissipation analysis of phase II testing is shown in Figure 11, where the ‘1st Half Energy’ and ‘2nd Half Energy’ denote the dissipated energy in the positive and negative direction, respectively. Moreover, the accumulated energy ratio could also be observed. For CFST-2-1 and CFST-2-2, the analysis result indicated that the loop energy suddenly dropped when entering into failure stage, accompanied by the rupture of the steel tube. The accumulated energy ratios of the two specimens revealed that the cumulative damage increased approximately linearly under constant amplitude loading. The half cycle energies of the positive and negative direction were not strictly equal, reflecting the existence of residual deformation and the Bauschinger effect. Regarding CFST-2-3 and CFST-2-4 under ‘variable pattern 2’, the peak energy dissipation at the maximum drift and the loop energy at the same drift decreased gradually, highlighting the development of cumulative damage caused by low-cycle fatigue. Figure 11(c) and (d) shows the wave-shaped advance trend of the accumulated energy ratio. In brief, great importance should be attached to the energy dissipation capacity under low-cycle fatigue of various loading histories.

Figure 11.

Energy dissipation analysis of phase I testing: (a) CFST-2-1, (b) CFST-2-2, (c) CFST-2-3 and (d) CFST-2-4.

Stiffness degradation

To depict the stiffness degradation, the secant stiffness used could be expressed as

K_{\sec}^{i} = (K_{\sec}^{i +} + K_{\sec}^{i -}) / 2

(6)

K_{\sec}^{i +} = F_{i}^{+} / Δ_{i}^{+}, K_{\sec}^{i -} = F_{i}^{-} / Δ_{i}^{-}

(7)

where $F_{i}^{+}$ and $F_{i}^{-}$ are the peak loads for the ith cycle in the two reversal directions, and $Δ_{i}^{+}$ and $Δ_{i}^{-}$ are the displacements corresponding to the peak load for the ith cycle in two directions. The label $K_{\sec}^{i}$ is the mean secant stiffness for the ith cycle.

Figure 12 graphically illustrates the stiffness degradation of the HCFTST columns. For the Q690 circular HCFTST columns in phase I testing, the increase in the axial compression ratio (n) tended to improve the initial stiffness, especially under D/t = 130. After the columns behaved nonlinearly, the stiffness degradation rate tended to be slow and showed no abrupt changes. In phase II testing, under the constant amplitude loading pattern, the specimen CFST-2-2 displayed apparent stiffness degradation compared to CFST-2-1 because of the larger drift ratio. Under ‘variable pattern 2’, the increase in the concrete strength increased the secant stiffness of CFST-2-3.

Figure 12.

Stiffness degradation: (a) phase I testing and (b) phase II testing.

Low-cycle fatigue life prediction

A more comprehensive understanding of low-cycle fatigue is to establish the fatigue life relationship of the columns. In this section, the low-cycle fatigue lives under different loading patterns were discussed in detail. A simplified fatigue life prediction method was proposed and verified for application in the performance evaluation of CFST columns.

Constant amplitude mode

The classical fatigue life prediction model proposed by Manson and Coffin (Coffin, 1953; Manson, 1953; Manson and Halford, 1981) is expressed as follows

\frac{Δ ε}{2} = \frac{Δ ε_{e}}{2} + \frac{Δ ε_{p}}{2} = \frac{{σ'}_{f}}{E} (2 N_{2 f})^{b} + ε'_{f} (2 N_{2 f})^{c}

(8)

where $Δ ε / 2$ , $Δ ε_{e} / 2$ and $Δ ε_{p} / 2$ are the total strain amplitude, elastic strain amplitude and plastic strain amplitude, respectively, and $σ'_{f}$ , $ε'_{f}$ , b and c are material parameters. E is the elasticity modulus, and $N_{2 f}$ is the fatigue life. The relationship between the strain amplitude and the fatigue life can be depicted in Figure 13, from which, it is noteworthy that, for the low-cycle fatigue problem, the plastic strain dominates the fatigue life.

Figure 13.

Strain amplitude–fatigue life relationship.

Considering the large error caused by strain measurement, instrument error and gradient variation in strain at different positions, the relationship in equation (8) was modified for convenience by ignoring the effect of elastic strain (EI-Bahy et al., 1999; Krawinkler et al., 1983) under low-cycle fatigue loading

N_{2 f} = C^{- 1} (Δ δ_{P})^{- c} or Δ δ_{P} = α (N_{2 f})^{χ}

(9)

where C, c, $α$ and $χ$ are material parameters. $Δ δ_{P}$ is the plastic deformation.

When offering two groups of data $(Δ δ_{P 1}, N_{2 f - 1})$ and $(Δ δ_{P 2}, N_{2 f - 2})$ , the parameters C and c ( $α$ or $χ$ ) in equation (9) could be determined as follows

c = \frac{\ln N_{2 f - 1} - \ln N_{2 f - 2}}{\ln Δ δ_{P 2} - \ln Δ δ_{P 1}}

(10)

C = \frac{1}{N_{2 f - 1} \cdot Δ δ_{P 1}^{c}} = \frac{1}{N_{2 f - 2} \cdot Δ δ_{P 2}^{c}}

(11)

α = C^{- 1 / c}, χ = - 1 / c

(12)

Regarding the aforementioned material parameters, some scholars considered them as constants for the same type columns (EI-Bahy et al., 1999; Gajalakshmi and Helena, 2012; Zhang et al., 2009a). The literature (Krawinkler et al., 1983) reveals that the parameter C has a greater fluctuation than that of c in equation (10). To recalibrate the parameter C for reducing the fluctuation as much as possible, it can be simplified to satisfy the function C = f(c) based on equation (11). Consequently, for the convenience of fatigue life prediction of CFST columns, based on statistical analysis of the previous test data (Zhang et al., 2009a, 2009b) and experimental data of this article, the parameter c can be proposed as follows

c = 5.9363 - 2.6058 K - 0.0119 (D / t)

(13)

K = 1 + 4.1 \frac{f_{r}}{f_{c}}

(14)

f_{r} = \frac{0.38 f_{y} \cdot t}{D - 2 t}

(15)

where K is the strength enhancement factor (Sakino et al., 2004) and $f_{r}$ is the confining stress.

The parameter C can be calculated according to Figure 14(a). Moreover, the variations in the two parameters versus the mean drift ratio $(\bar{δ})$ between different columns could be depicted in Figure 14(b) and (c). It could be speculated from the data that the scatter band was of uniform width along the regression line, indicating that the uncertainty in life prediction can be ascribed to that phenomenon. Therefore, the fatigue life of CFST columns could be predicted using equation (9).

Figure 14.

Variations in material parameters: (a) calculation of parameter C, (b) variation in C and (c) variation in c.

To validate the accuracy of the simplified method aforementioned, the test data from other research studies (Gajalakshmi and Helena, 2012) were also used to verify the prediction result of the fatigue life, as shown in Figure 15. From the result of the simplified method without considering the variations in the material parameters in Figure 15(a), the mean value and variance are 1.120 and 0.197, respectively, and most data are concentrated in the 0.25 error zone. When considering the variations in the material parameters in Figure 15(b), the mean value and variance are reduced to 1.064 and 0.079, respectively. It can be concluded that the simplified prediction method is capable of predicting the low-cycle fatigue life of circular CFST columns, and the changes in material parameters under different loading history should not be neglected, especially for cyclic loading.

Figure 15.

Fatigue life prediction results of the simplified method: (a) prediction result without variations and (b) prediction result considering variations.

Variable amplitude mode

In fact, the structures could not be subject to the constant amplitude deformation under earthquake motions. Therefore, an alternative method should be developed to transform the variable amplitudes to constant amplitudes for the convenience of low-cycle fatigue life evaluation. Based on the energy equivalence principle (McCabe and Hall, 1989), the low-cycle fatigue lives of specimens under variable amplitude patterns can be equivalent to the constant amplitude patterns as follows

N_{2 f} = \frac{E_{T}}{F_{y} \cdot Δ δ}

(16)

where $E_{T}$ is the total dissipated hysteretic energy, $F_{y}$ is the yield resistance and $Δ δ$ is the lateral deformation. As shown in Table 6, all the tested specimens under variable loading amplitude in this study were transformed to constant amplitude patterns with different drift ratios. From the equivalent results, the Q690 circular HCFTST columns displayed favourable anti-fatigue ability under low-cycle loading.

Table 6.

Equivalent hysteretic cycles.

Loading patterns	Specimens	$E_{T} (kN m)$	F_y (kN)	Fatigue life (Δδ = 2%)	Fatigue life (Δδ = 4%)	Fatigue life (Δδ = 6%)
Variable pattern 1	CFST-1-1	76.96	99.72	74	37	25
	CFST-1-2	68.51	92.22	71	35	24
	CFST-1-3	159.12	261.86	58	29	19
	CFST-1-4	87.73	260.00	32	16	11
Variable pattern 2	CFST-2-3	42.09	92.22	43	22	14
Variable pattern 2	CFST-2-4	42.47	74.14	55	27	18

CFST: concrete-filled steel tubular.

Conclusion

This article presented the results of an experimental study of the hysteresis behaviour of Q690 circular HCFTST columns. Through the detailed investigation, the following conclusions can be drawn within the scope of this study:

For the Q690 circular HCFTST columns with out-of-code D/t ratios, the failure modes include concrete crushing, severe rupture and local buckling of the steel tube at the column bases. The elephant foot shaped buckling could be observed at nearly the same heights (H = 20 mm) above the foundation surface.

The columns with D/t = 130, the lower axial compression ratio (n) could result in the weak energy dissipation capacity due to the loss of confined effect. Increasing axial compression ratio is an efficient method to motivate the potential of HS materials for offering an excellent confined action to limit the propagation of the concrete shear cracks.

The Q690 circular HCFTST columns could exhibit favourable hysteretic performance and large lateral deformation capacity. The elastic and the elastic–plastic inter-story drifts of the columns are, respectively, $θ_{y} = (0.0276 - 0.0344)$ and $θ_{u} = (0.0700 - 0.0907)$ . Overall, this result satisfies the ductility requirement in some aseismic region.

The strength reduction in phase II testing is not due to the imposed displacement beyond the ultimate value, but due to the cumulative damage induced by the low-cycle fatigue under cyclic loading. The loading history determines the developmental tendency of the dissipated energy and the cumulative damage.

In phase I testing, the increase in the axial compression ratio (n) tends to improve the initial secant stiffness under D/t = 130. In phase II testing, under the constant amplitude loading pattern, the larger drift ratio could lead to rapid degradation of the stiffness and strength. Under ‘variable pattern 2’, the increase in concrete strength could increase the secant stiffness of CFST-2-3.

A simplified fatigue life prediction method is proposed and verified and is capable of predicting the low-cycle fatigue life of circular CFST columns, and the changes in material parameters under different loading history should not be neglected, especially for cyclic loading.

In brief, the Q690 circular HCFTST columns with reasonable design could display favourable hysteretic and anti-fatigue abilities and could be expected to have widespread application in earthquake-prone regions.

Footnotes

Acknowledgements

The authors are also grateful to everyone participating in this experimental programme for their selfless assistance.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This research work was financially supported by the National Natural Science Foundation of China (grant no. 11172226); their support was gratefully acknowledged.

ORCID iD

Jiantao Wang

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